section 1-5
DESCRIPTION
Solving EquationsTRANSCRIPT
Section 1-5Solving Equations
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
x = 450
Warm-upMatt Mitarnowski won a raffle. He put one third of his
winnings into the bank, used one half of the money for a car payment, and used the rest to buy some comic
books. If Matt spent $75 on comics, how much money did he win?
x = money won
13
x + 12
x + 75 = x
56
x + 75 = x
75 = 16
x
6i75 = 16
xi6
x = 450
Matt won $450.
What did we do to solve this problem?
What did we do to solve this problem?
Read the problem
What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
Solve
What did we do to solve this problem?
Read the problem
Make sure to solve for what is being asked
Identify variables
Set up the problem
Solve
Answer the question
Example 13x + 7 = 25
Example 13x + 7 = 25
-7
Example 13x + 7 = 25
-7 -7
Example 13x + 7 = 25
-7 -7
Example 13x + 7 = 25
-7 -7
3x
Example 13x + 7 = 25
-7 -7
3x =
Example 13x + 7 = 25
-7 -7
3x = 18
Example 13x + 7 = 25
-7 -7
3x = 183 3
Example 13x + 7 = 25
-7 -7
3x = 183 3
x = 6
Distributive Property:
Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
For real numbers a, and b:
-(a + b) = -a + -b
Distributive Property: For real numbers a, b, and c:
c(a + b) = ac + bc
Opposite of a Sum Theorem:
For real numbers a, and b:
-(a + b) = -a + -b
Note: The “-” here stands for “opposite”
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
49 = 7x
Example 2
f (x ) = 5x − (3 − 2x ) Suppose f (x ) = 46 Find x..
46 = 5x − (3 − 2x )
46 = 5x − 3 + 2x
46 = 7x − 3
49 = 7x
x = 7
Clearing out fractions
Clearing out fractions
Face it, most of you hate them, so how do you get rid of them?
Clearing out fractions
Face it, most of you hate them, so how do you get rid of them?
Multiply both sides of the equation by a common denominator
Example 3
Example 3
16
a + 25
a +10 = 346
Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
17a = 10080
Example 3
16
a + 25
a +10 = 346
30( 16
a + 25
a +10) = 30(346)
5a +12a + 300 = 10380
17a + 300 = 10380
17a = 10080
a =
10080
17
Example 4
.04b + .08(b − 3) = 12
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
12b = 1224
Example 4
.04b + .08(b − 3) = 12
100[.04b + .08(b − 3)] = 100(12)
4b + 8(b − 3) = 1200
4b + 8b − 24 = 1200
12b − 24 = 1200
12b = 1224
b = 102
Homework
Homework
p. 33 #1 - 27